2/28/2016
Physics 2D
PHYS 342 Modern Physics
Atom I: Rutherford Model and Bohr Model
Subfields in Modern Physics
(Large to Small):
Cosmology
Condensed Matter Physics
Atomic, molecular, and optical physics
Nuclear physics
High energy (particle) physics
……..
Today Contents:
a) Basic Properties of Atoms b) Rutherford Model and Scattering Experiments
c) Bohr Model and Line Spectra
Our Second Topic
HISTORY OF THE ATOM
HISTORY OF THE ATOM
Ancient Greek philosopher, Democritus, formulated an atomic theory for the universe
1808
440 BC
John Dalton
He pounded up materials in his mortar and
suggested that all matter was made up of
pestle until he had reduced them to smaller
tiny spheres that were able to bounce around
and smaller particles which he called
with perfect elasticity and called them
ATOMS)
ATOMS
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HISTORY OF THE ATOM
1898
Thomson’s Apparatus to Discover Electrons
Joseph John Thompson
found that matter could sometimes eject a
far smaller negative charged particle which
he called an
ELECTRON
https://www.youtube.com/watch?v=o1z2S3ME0cI
Thomson’s Apparatus to Discover Electrons
Atoms and Radioactivity
Atoms are not indestructible.
Atoms are composed of smaller particles
Unstable Atoms and
Devised an experiment to find the ratio of the cathode ray
particle’s mass (me) to the charge (e)
me /e = –5.686 x 10–12 kg C–1
Based upon the mass to charge ratio, the electron
must be much smaller than the atom
Evidence: Radioactivity
Alpha particles – positively charged
Beta particles – negatively charged
Gamma rays – no charge
……..
mH+ /e = 1.044 x 10–8 kg C–1
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Mass Spectrometer
If a stream of positive ions
having equal velocities is
brought into a magnetic
field, the lightest ions are
deflected the most, making
a tighter circle
A record of the
mass to charge
ratio is called a
mass spectrum
Proton and Neutron
Isotopes of Neon
By analyzing the emitted particles from unstable atoms, people found proton and neutron
Electron Wave Function
Proton: positive charge +e, mass is about
mP= 1.67265 x 10–27 kg
(determined by
3D time-dependent
Schrodinger Equations)
Neutron: no charge, mass is about
mN= 1.67495 x 10–27 kg
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Rutherford Scattering Experiments
Ernest Rutherford
1910
a) Basic Properties of Atoms b) Rutherford Model and Scattering Experiments
c) Bohr Model and Line Spectra
Most the alpha particles (helium nuclei) pass Rutherford’s
through the gold foil


Nuclear Model of the Atom
Atom mostly empty space
Alpha particles did not hit anything
A very few deflected straight back

Alpha particles deflected by a dense positive nucleus
https://www.youtube.com/watch?v=XBqHkraf8iE
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Quantitative Calculation about Scattering
Scattering Probability
Incoming particles scattered by the nuclei in an atom. 1
,
4
The path of the scattered particle is a hyperbola. Smaller impact parameters b
give large scattering angles. 1 1
sin
cos
1
8
Find the relation between the impact parameter and scatting angle. ,
The impact factor b and the scattering angle θ has one‐to‐one correspondence. If particle enters the atom within the disc area πb2 , the scattering angle will be larger than θ. What is the probability?
and are the density and the molar mass, and t is the thickness of foil. The nuclei per unit volume is
,
is Avogadro’s number
The nuclei per unit area is
ICP21. Prove it!
The fraction scatter at an angle larger than θ.
2 4
cot
2
Differential Scattering Probability
The detector is located at the angle and the distance r, what is the detection probability? (We need to know the scattering probability per unit area for the angle and the distance r.)
2 sin
2 4
cot
2
a) Basic Properties of Atoms b) Rutherford Model and Scattering Experiments
c) Bohr Model and Line Spectra
1
4
2 4
sin
2
Rutherford Scattering Formula
(remarkably good in experiments!)
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The Electromagnetic Spectrum
Emission Spectrum
Emission Spectrum of Hydrogen
1 nm = 1 x 10-9 m = “a billionth of a meter”
410 nm 434 nm
486 nm
656 nm
Continuous and Line Spectra
Visible
spectrum
light
(nm)
400
450
500
550
600
650
700
750 nm
Emission Spectra of
Different Atoms: A
Fingerprint to Identify
Na
H
Ca
Hg
o
4000 A
5000
6000
7000
Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.
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Rydberg
and Balmer
(1886)
Rydberg
Equation
Rydberg Equation
1/λ
‐ 1/n2]
RH = 1.09678 x 10‐2 nm‐1
n0=1,2,3,… and n=n0+1, n0+2….
= RH [1/n02
A mathematical equation that fits the data for
hydrogen emission spectrum.
n0=1 At that time, electron had no yet been discovered,
so there is no microscopic model to explain the
observed wavelengths.
n0=2 n0=3
n0=4 n0=5 Bohr’s Model of the Atom (1910)
Bohr’s Model of the Atom (1910)
1)Assume electrons orbit nucleus in circular orbits
2)Propose the energy of the orbit is proportional to the distance from the nucleus (increasing distance – increasing energy)
When the atom absorbs energy


3)Assume only certain allowable energies (Energy Quantization!)
4)Used quantized angular momentum to calculate the allowable energy
Electron falls back down to lower levels


Niels Bohr
(1885-1962)
Electron moves up to higher energy with more potential energy farther away from nucleus
Unstable with higher PE

Energy released
PE converted to KE as electron fall
The color of light observed reflects the energy released in the fall
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Bohr’s Model of the Atom
Bohr’s Model of the Atom
Bohr Model was suggested before people established quantum mechanics (Schrodinger Eq).
So it uses “classical mechanics” + “quantization condition”. Such theories are also called “ semi‐
classical theory”.
(Z=1 for hydrogen)
“quantization condition”.
1,2. .
ICP22. Prove it!
(Z=1 for hydrogen)
and
Bohr radius .
Ground State of H
- 13.60 eV
Bohr’s Calculations of the Energy
Visualizing the Movement of the
Electron
∆E = - 13.60 eV (1/nf2 – 1/ni2)
n = the energy level
∆E = positive when electron climbs up levels
absorbing energy
increasing PE
∆E = negative when e- falls down levels
releasing energy
decreasing PE
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HW 6:
Chapter 6----8,18,28, 37
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